The unexpected gesture was seen as a response to critics who predicted that the Muslim Brotherhood would abandon Egypt’s peace treaty with Israel in pursuit of a policy of Islamic radicalism.

President Mohammed Morsi replied to a letter of congratulations on his election by the Israeli president, Shimon Peres.

Mr Morsi, who was elected president at the end of June, pledged to work towards reviving the Middle East peace process.

Significantly, he also referenced Israeli security concerns in a conscious attempt to address an issue that Benjamin Netanyahu, Israel’s prime minister, has repeatedly emphasised must be the hinge on which a peace deal with the Palestinians is built.

“I am looking forward to exerting our best efforts to get the Middle East peace process back to its right track in order to achieve security and stability for all peoples of the region, including (the) Israeli people,” he said.

Israel’s peace treaty with Egypt, signed after the historic Camp David accords of 1978, is seen as vital to stability in the Middle East and has ensured that there has been no Arab invasion of the Jewish state for nearly 40 years.

The Brotherhood is formally linked to Hamas, the militant group which refuses to recognise Israel’s right to exist, and although Mr Morsi’s letter is careful to refer to the “Israeli people” rather than the country itself it is clearly intended to reassure.

Mr Morsi has said he would not rescind Egypt’s peace treaty with Israel but has balanced that stance with easing Egypt’s support for the Israeli blockade of Gaza, which Hamas controls. He has also regularly met Hamas leaders.

Currently, defence and security policy is still firmly in the hands of the military rather than the presidency as part of Egypt’s muted democratic transition. But the army and the Brotherhood appear to be working closely together – an increase in fuel supplies to Gaza was announced first under the Supreme Council of the Armed Forces and then taken on by President Morsi.

Leon Panetta, the US defence secretary, met Mr Morsi and the chairman of SCAF, Field Marshal Hossein Tantawi, yesterday and said he thought the two men had “a very good working relationship and are working together for the same ends”.